Documentation

# csch

Hyperbolic cosecant

## Description

example

Y = csch(X) returns the hyperbolic cosecant of the elements of X. The csch function operates element-wise on arrays. The function accepts both real and complex inputs. All angles are in radians.

## Examples

collapse all

Create a vector and calculate the hyperbolic cosecant of each value.

X = [0 pi 2*pi 3*pi];
Y = csch(X)
Y = 1×4

Inf    0.0866    0.0037    0.0002

Plot the hyperbolic cosecant over the domain $-\pi and $0

x1 = -pi+0.01:0.01:-0.01;
x2 = 0.01:0.01:pi-0.01;
y1 = csch(x1);
y2 = csch(x2);
plot(x1,y1,x2,y2)
grid on

## Input Arguments

collapse all

Input angles in radians, specified as a scalar, vector, matrix, or multidimensional array.

Data Types: single | double
Complex Number Support: Yes

collapse all

### Hyperbolic Cosecant

The hyperbolic cosecant of x is equal to the inverse of the hyperbolic sine

$\text{csch}\left(x\right)=\frac{1}{\mathrm{sinh}\left(x\right)}=\frac{2}{{e}^{x}-{e}^{-x}}.$

In terms of the traditional cosecant function with a complex argument, the identity is

$\text{csch}\left(x\right)=i\mathrm{csc}\left(ix\right)\text{\hspace{0.17em}}.$